Solve 7x^2 8x - 3 = 0

Question

Solve the equation

x = \frac{3 147}{14}

Alternative Form

x \approx 0.376974

Evaluate

7 x^{2} \times 8 x - 3 = 0

Multiply

More Steps

Evaluate

7 x^{2} \times 8 x

Multiply the terms

56 x^{2} \times x

Multiply the terms with the same base by adding their exponents

56 x^{2 + 1}

Add the numbers

56 x^{3}

56 x^{3} - 3 = 0

Move the constant to the right-hand side and change its sign

56 x^{3} = 0 + 3

Removing 0 doesn't change the value,so remove it from the expression

56 x^{3} = 3

Divide both sides

\frac{56 x ^{3}}{56} = \frac{3}{56}

Divide the numbers

x^{3} = \frac{3}{56}

Take the 3 -th root on both sides of the equation

3 x^{3} = 3 \frac{3}{56}

Calculate

x = 3 \frac{3}{56}

Solution

More Steps

Evaluate

3 \frac{3}{56}

To take a root of a fraction,take the root of the numerator and denominator separately

\frac{3 3}{3 56}

Simplify the radical expression

More Steps

Evaluate

356

Write the expression as a product where the root of one of the factors can be evaluated

3 8 \times 7

Write the number in exponential form with the base of 2

3 2^{3} \times 7

The root of a product is equal to the product of the roots of each factor

3 2^{3} \times 37

Reduce the index of the radical and exponent with 3

237

\frac{3 3}{2 3 7}

Multiply by the Conjugate

\frac{3 3 \times 3 7 ^{2}}{2 3 7 \times 3 7 ^{2}}

Simplify

\frac{3 3 \times 3 49}{2 3 7 \times 3 7 ^{2}}

Multiply the numbers

More Steps

Evaluate

33 \times 349

The product of roots with the same index is equal to the root of the product

3 3 \times 49

Calculate the product

3147

\frac{3 147}{2 3 7 \times 3 7 ^{2}}

Multiply the numbers

More Steps

Evaluate

237 \times 3 7^{2}

Multiply the terms

2 \times 7

Multiply the terms

14

\frac{3 147}{14}

x = \frac{3 147}{14}

Alternative Form

x \approx 0.376974

Show Solution